Bianchi type electromagnetic cosmology - Type I Hamiltonian

Ryan, Michael P.; Waller, S. M.; Shepley, L. C.

doi:10.1086/159750

Cited by 42 publications

(67 citation statements)

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“…• Moreover, it assumes the results established in [29,30], where N = 1 supergravity was shown to constitute a natural "square-root" of gravity in a Dirac-like manner: the analysis of a second order equation of the Klein-Gordon type (i.e., the Wheeler-DeWitt equation) could be substituted by that of a supersymmetric induced set of first order differential equations. This would then have profound consequences (see, e.g., [1,2]) regarding the dynamics of the wave function of the universe (this approach improved a previous attempt solely based on general relativity [33], without any supersymetric considerations).…”

Section: Introductionmentioning

confidence: 92%

“…The programme of research in SQC imports some of its guidelines from earlier investigations in quantum supergravity [19][20][21][22][23][24][25][26][27][28] using canonical methods [29][30][31][32][33][34]. It has been gradually enlarged, employing many cosmological scenarios extensively reported in the published literature [1][2][3][4][5][6][7][8][9][10][11][12], with the following properties enhacing a significant motivation:…”

Section: Introductionmentioning

confidence: 99%

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FRW minisuperspace with local N=4 supersymmetry and self-interacting scalar field

Moniz¹

2003

Ann. Phys.

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A supersymmetric FRW model with a scalar supermultiplet and generic superpotential is analysed from a quantum cosmological perspective. The corresponding Lorentz and supersymmetry constraints allow to establish a system of first order partial differential equations from which solutions can be obtained. We show that this is possible when the superpotential is expanded in powers of a parameter λ 1. At order λ 0 we find the general class of solutions, which include in particular quantum states reported in the current literature. New solutions are partially obtained at order λ 1 , where the dependence on the superpotential is manifest. These classes of solutions can be employed to find states for higher orders in λ. Our analysis further points to the following: (i) supersymmetric wave functions can only be found when the superpotential has either an exponential behaviour, an effective cosmological constant form or is zero; (ii) If the superpotential behaves differently during other periods, the wave function is trivial (Ψ FRW SUSY = 0, i.e., no supersymmetric states). We conclude this paper discussing how our FRW minisuperspace (with N = 4 supersymmetry and invariance under time-reparametrization) can be relevant concerning the issue of supersymmetry breaking.

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Section: Introductionmentioning

confidence: 92%

Section: Introductionmentioning

confidence: 99%

FRW minisuperspace with local N=4 supersymmetry and self-interacting scalar field

Moniz¹

2003

Ann. Phys.

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“…Let us now consider a homogeneous 3-manifold of one of the Bianchi types; then there exists an invariant basis of one-forms ω p = ω p i (x) dx i , such that any homogeneous tensor field on the manifold has spatially constant components when expanded in this basis [20,21]. In particular, we have…”

Section: A Metric Representation Of the Constraint Equationsmentioning

confidence: 99%

Chern-Simons state for the nondiagonal Bianchi type IX model

Paternoga

Graham

1998

Phys. Rev. D

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The Bianchi IX mixmaster model is quantized in its non-diagonal form, imposing spatial diffeomorphism, time reparametrization and Lorentz invariance as constraints on physical state vectors before gauge-fixing. The result turns out to be different from quantizing the diagonal model obtained by gauge-fixing already on the classical level. For the non-diagonal model a generalized 9-dimensional Fourier transformation over a suitably chosen manifold connects the representations in metric variables and in Ashtekar variables. A space of five states in the metric representation is generated from the single physical Chern-Simons state in Ashtekar variables by choosing five different integration manifolds, which cannot be deformed into each other. For the case of a positive cosmological constant Λ we extend our previous study of these five states for the diagonal Bianchi IX model to the non-diagonal case. It is shown that additional discrete (permutation) symmetries of physical states arise in the quantization of the non-diagonal model, which are satisfied by two of the five states connected to the Chern-Simons state. These have the characteristics of a wormhole groundstate and a Hartle-Hawking 'no-boundary' state, respectively. We also exhibit a special gauge-fixing of the time reparametrization invariance of the quantized system and define an associated manifestly positive scalar product. Then the wormhole ground state is left as the only normalizable physical state connected to the Chern-Simons state.

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“…For dust (γ = 1, a case discussed in [18]) and stiff (γ = 2) perfect fluids this equation is linear and can be explicitly solved. For some other values of γ (namely 5 4 , 4 3 , 3 2 , 5 3 , 7 4 ), it reduces to at most a fourth degree polynomial equation which can be explicitly solved in principle.…”

Section: Spatially Homogeneous Class a Models Belonging To The Symmetmentioning

confidence: 99%

Exact hypersurface-homogeneous solutions in cosmology and astrophysics

1995

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A framework is introduced which explains the existence and similarities of most exact solutions of the Einstein equations with a wide range of sources for the class of hypersurface-homogeneous spacetimes which admit a Hamiltonian formulation. This class includes the spatially homogeneous cosmological models and the astrophysically interesting static spherically symmetric models as well as the stationary cylindrically symmetric models. The framework involves methods for finding and exploiting hidden symmetries and invariant submanifolds of the Hamiltonian formulation of the field equations. It unifies, simplifies, and extends most known work on hypersurface-homogeneous exact solutions. It is shown that the same framework is also relevant to gravitational theories with a similar structure, such as Brans-Dicke or higher-dimensional theories. PACS number(s): 04.20.Jb, 98.80.H~ Saunders [42] (t = -1) McVittie 1671 (E = 1) Datta 1681 ( t = --I) Bonnor [69] (E = 1) Jacobs [70] (t = -1) Ruban [71] ( t = -1) Barnes [72] (E -= -1) ---Nord. 1781 ( t = 1) K-S [73] ( t = -1) Datta [74] (t = 1) --K-S [73] ( t = -1) Schwar. [75] (e = 1 ) Taub [6] ( E = -1) Taub [6] ( t = -1) Kottler [76] ( t = 1) Brill [60] (E = --1) Reissner [77] ( t = 1)

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Bianchi type electromagnetic cosmology - Type I Hamiltonian

Cited by 42 publications

References 0 publications

FRW minisuperspace with local N=4 supersymmetry and self-interacting scalar field

FRW minisuperspace with local N=4 supersymmetry and self-interacting scalar field

Chern-Simons state for the nondiagonal Bianchi type IX model

Exact hypersurface-homogeneous solutions in cosmology and astrophysics

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